Question

The principal value of the argument of the complex number 1 –i is ____________.

Answer 1

Since z = 1 – i = 1 + i(–1)
$$\begin{gathered} \mathrm{here}\theta ={\tan }^{-1}\left|\frac{-1}{1}\right| \\ \theta ={\tan }^{-1}1=\frac{\mathrm{\pi }}{y} \end{gathered}$$
Since z lies in 4^th quadrant.
∴argument is given by $\frac{-\mathrm{\pi }}{y}$